Quadratic Spline Interpolation Part 1 of 2

Quadratic Spline Example The upward velocity of a rocket is given as a function of time. Using quadratic splines a) Find the velocity at t=16 seconds b) Find the acceleration at t=16 seconds c) Find the distance covered between t=11 and t=16 seconds tv(t) sm/s

Data and Plot tv(t) sm/s

Solution Let us set up the equations

Each Spline Goes Through Two Consecutive Data Points

tv(t) sm/s Each Spline Goes Through Two Consecutive Data Points

Derivatives are Continuous at Interior Data Points

Derivatives are continuous at Interior Data Points At t=10 At t=15 At t=20 At t=22.5

Last Equation

Final Set of Equations

Coefficients of Spline iaiai bibi cici

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Quadratic Spline Interpolation Part 2 of 2

Final Solution

Velocity at a Particular Point a) Velocity at t=16

Acceleration from Velocity Profile b) Acceleration at t=16

Acceleration from Velocity Profile The quadratic spline valid at t=16 is given by,

Distance from Velocity Profile c) Find the distance covered by the rocket from t=11s to t=16s.

Distance from Velocity Profile

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